{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:YZ2GKCUD4OQJUFL2MHM4XOWOGQ","short_pith_number":"pith:YZ2GKCUD","schema_version":"1.0","canonical_sha256":"c674650a83e3a09a157a61d9cbbace341ff1bd624c4356ded63417d6c36210ea","source":{"kind":"arxiv","id":"1307.7081","version":1},"attestation_state":"computed","paper":{"title":"3-extremal holomorphic maps and the symmetrised bidisc","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Jim Agler, N. J. Young, Zinaida A. Lykova","submitted_at":"2013-07-26T15:55:46Z","abstract_excerpt":"We analyse the 3-extremal holomorphic maps from the unit disc $\\mathbb{D}$ to the symmetrised bidisc $ \\mathcal{G}$, defined to be the set $ \\{(z+w,zw): z,w\\in\\mathbb{D}\\}$, with a view to the complex geometry and function theory of $\\mathcal{G}$. These are the maps whose restriction to any triple of distinct points in $\\mathbb{D}$ yields interpolation data that are only just solvable. We find a large class of such maps; they are rational of degree at most 4. It is shown that there are two qualitatively different classes of rational $\\mathcal{G}$-inner functions of degree at most 4, to be call"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1307.7081","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-07-26T15:55:46Z","cross_cats_sorted":[],"title_canon_sha256":"12462832976179d1455dff1e26949d9a7e292c150837f3ccf35bd9918100dc08","abstract_canon_sha256":"0ddbfa538d12c3e0424d8c09ae6ae8b3eb412c44a878bde112e5e5af27d8190e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:25.389282Z","signature_b64":"SWGbF6Ez8TqOcKXeqorGkhc4NnsU52aapMb36SQ7homxi56dRBJU7VW7VRGgAaRWHS2bJ2dox/Xs85KbU4hWAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c674650a83e3a09a157a61d9cbbace341ff1bd624c4356ded63417d6c36210ea","last_reissued_at":"2026-05-18T03:17:25.388738Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:25.388738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"3-extremal holomorphic maps and the symmetrised bidisc","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Jim Agler, N. J. Young, Zinaida A. Lykova","submitted_at":"2013-07-26T15:55:46Z","abstract_excerpt":"We analyse the 3-extremal holomorphic maps from the unit disc $\\mathbb{D}$ to the symmetrised bidisc $ \\mathcal{G}$, defined to be the set $ \\{(z+w,zw): z,w\\in\\mathbb{D}\\}$, with a view to the complex geometry and function theory of $\\mathcal{G}$. These are the maps whose restriction to any triple of distinct points in $\\mathbb{D}$ yields interpolation data that are only just solvable. We find a large class of such maps; they are rational of degree at most 4. It is shown that there are two qualitatively different classes of rational $\\mathcal{G}$-inner functions of degree at most 4, to be call"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7081","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1307.7081","created_at":"2026-05-18T03:17:25.388812+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.7081v1","created_at":"2026-05-18T03:17:25.388812+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7081","created_at":"2026-05-18T03:17:25.388812+00:00"},{"alias_kind":"pith_short_12","alias_value":"YZ2GKCUD4OQJ","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"YZ2GKCUD4OQJUFL2","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"YZ2GKCUD","created_at":"2026-05-18T12:28:09.283467+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YZ2GKCUD4OQJUFL2MHM4XOWOGQ","json":"https://pith.science/pith/YZ2GKCUD4OQJUFL2MHM4XOWOGQ.json","graph_json":"https://pith.science/api/pith-number/YZ2GKCUD4OQJUFL2MHM4XOWOGQ/graph.json","events_json":"https://pith.science/api/pith-number/YZ2GKCUD4OQJUFL2MHM4XOWOGQ/events.json","paper":"https://pith.science/paper/YZ2GKCUD"},"agent_actions":{"view_html":"https://pith.science/pith/YZ2GKCUD4OQJUFL2MHM4XOWOGQ","download_json":"https://pith.science/pith/YZ2GKCUD4OQJUFL2MHM4XOWOGQ.json","view_paper":"https://pith.science/paper/YZ2GKCUD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.7081&json=true","fetch_graph":"https://pith.science/api/pith-number/YZ2GKCUD4OQJUFL2MHM4XOWOGQ/graph.json","fetch_events":"https://pith.science/api/pith-number/YZ2GKCUD4OQJUFL2MHM4XOWOGQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YZ2GKCUD4OQJUFL2MHM4XOWOGQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YZ2GKCUD4OQJUFL2MHM4XOWOGQ/action/storage_attestation","attest_author":"https://pith.science/pith/YZ2GKCUD4OQJUFL2MHM4XOWOGQ/action/author_attestation","sign_citation":"https://pith.science/pith/YZ2GKCUD4OQJUFL2MHM4XOWOGQ/action/citation_signature","submit_replication":"https://pith.science/pith/YZ2GKCUD4OQJUFL2MHM4XOWOGQ/action/replication_record"}},"created_at":"2026-05-18T03:17:25.388812+00:00","updated_at":"2026-05-18T03:17:25.388812+00:00"}